Problem: What do the following two equations represent? $2x+5y = -3$ $-2x-5y = -3$
Explanation: Putting the first equation in $y = mx + b$ form gives: $2x+5y = -3$ $5y = -2x-3$ $y = -\dfrac{2}{5}x - \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $-2x-5y = -3$ $-5y = 2x-3$ $y = -\dfrac{2}{5}x + \dfrac{3}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.